Structural mode shape alignment

ABSTRACT

A method is disclosed for reducing noise and vibration within a structure of a mobile platform, wherein the noise and vibration are at least in part caused by airflow over an outer skin of the mobile platform parallel to a longitudinal line extending fore to aft along the structure. The method may involve forming the structure such that a fundamental panel vibration mode shape of the structure is not parallel to the longitudinal line.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.10/846,861 filed on May 14, 2004. The entire disclosure of the aboveapplication is incorporated herein by reference.

FIELD OF THE INVENTION

The present invention relates to systems and methods for amelioratingnoise, and more particularly, to a system and method for amelioratingnoise within a high speed mobile platform, in which the noise is causedin large part by the turbulent boundary layer air flow over a skin panelstructure of the mobile platform.

BACKGROUND OF THE INVENTION

With various forms of commercial platforms in which passengers aretransported, minimizing noise inside a cabin of the mobile platform isan important consideration. In applications involving commercialpassenger aircraft, this is an especially important consideration. Thecabin noise within a commercial aircraft is caused at least in part bythe turbulent boundary layer flow over the skin of the aircraft. This isespecially so when the aircraft is traveling at cruise speeds (e.g.,around 500 mph or slightly greater), and at an area within the fuselagegenerally between the nose and wings.

It would be highly advantageous and desirable if an additional degree ofnoise reduction could be accomplished without simply adding additionalinsulation into the construction of a fuselage or other cabin-likestructure of a high speed mobile platform. As will be appreciated, theadding of insulation increases the weight of the mobile platform, aswell as its cost of manufacture. The additional weight added to themobile platform by simply adding extra insulating material into thefuselage also increases the overall weight of the mobile platform, andtherefore contributes to a reduction in fuel economy.

In one aspect the present disclosure relates to a method for reducingnoise and vibration within a structure of a mobile platform, wherein thenoise and vibration are at least in part caused by airflow over an outerskin of the mobile platform parallel to a longitudinal line extendingfore to aft along the structure. The method may comprise forming thestructure such that a fundamental panel vibration mode shape of thestructure is not parallel to the longitudinal line.

In another aspect the present disclosure relates to a method forreducing noise within a mobile platform, wherein the noise is at leastin part caused by a turbulent boundary layer flow of air over an outersurface of a skin of the mobile platform. The method may compriseforming a fuselage of the mobile platform with a plurality of stringersand a plurality of frame members. The fuselage may be further formed sothat both the plurality of stringers and the plurality of frame membersare oriented at non-parallel to a longitudinal axis extending fore toaft along the fuselage. A skin may be secured to at least a subpluralityof the stringers and a subplurality of the frame members, for supportingthe skin. The structure may be further assembled such that the structureis fastened to and supports the skin to provide a fundamental vibrationmode shape for the skin that is not parallel to a direction of flow ofthe turbulent boundary layer flow.

In still another aspect a method is disclosed for reducing noise andvibration within a fuselage of a mobile platform, wherein the noise andvibration are at least in part caused by airflow over an outer skin ofthe mobile platform parallel to a longitudinal line extending fore toaft along the fuselage of the mobile platform. The method may compriseforming a fuselage with a plurality of stringers and a plurality offrame members such that at least one of the plurality of stringers orthe plurality of frame members is oriented parallel to the longitudinalline. The fuselage may be formed with a plurality of stiffening membersthat are oriented at an angle non-parallel to the longitudinal line,non-parallel to the plurality of stringers and non-parallel to theplurality of frame members. A skin panel may be secured to thepluralities of stringers, frame members and stiffening members. Thenon-parallel orientation of the stiffening members relative to thelongitudinal line is used to create a fundamental panel vibration modeshape for the skin of the fuselage that is not parallel to thelongitudinal line, to cause a noise reduction within an interior area ofthe fuselage of noise generated by airflow over the skin of the fuselagewhile the mobile platform is in flight.

SUMMARY OF THE INVENTION

The features, functions, and advantages can be achieved independently invarious embodiments of the present inventions or may be combined in yetother embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will become more fully understood from thedetailed description and the accompanying drawings, wherein:

FIG. 1 is a simplified representation of a portion of a prior artfuselage of a mobile platform illustrating the fundamental panelvibration mode shape produced by the arrangement of the stringers andframe members, and where the fundamental panel vibration mode shape isdirected generally parallel to the direction of the turbulent boundarylayer flow;

FIG. 2 is an illustration of a representative portion of the fuselage ofan aircraft in which the stringers and frame members are coupledperpendicular to one another, but where the stringers are arrangednon-parallel relative to a direction of a turbulent boundary layer flow,and thus produce a fundamental panel vibration mode shape that is at anangle non-parallel to the direction of the turbulent boundary layerflow;

FIG. 3 is an alternative preferred form of the fuselage in whichdiagonal stiffening members are incorporated to provide a fundamentalpanel vibration mode shape which is aligned non-parallel to thedirection of the turbulent boundary layer flow;

FIG. 4 is a diagram for assisting in the description of the turbulentboundary layer coordinate transformation;

FIG. 5 is a diagram for assisting in the description of the jointacceptance function for the fundamental panel vibration mode shape;

FIG. 6 is a graph illustrating the panel response as a function of flowangle and the decibel level reduction achieved by the panel response;

FIG. 7 is a graph of the longitudinal component of the joint acceptanceas a function of the mobile frequency;

FIG. 8 is a graph of the lateral component of the joint acceptance as afunction of mobile frequency; and

FIG. 9 is a graph of the dB reduction relative to the frequency excitingthe fundamental panel vibration mode; and

FIG. 10 is an exemplary illustration of the teachings of the presentdisclosure applied to a window belt region of a commercial jet aircraft.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The following description of the preferred embodiment(s) is merelyexemplary in nature and is in no way intended to limit the invention,its application, or uses.

Referring to FIG. 1, there is shown a prior art illustration of arepresentative portion of a fuselage 10 of a mobile platform, in thisexample a commercial jet aircraft, in accordance with a prior artconstruction of the fuselage. The fuselage 10 incorporates a pluralityof stringers 12 and frame members 14 that support a skin panel 16. Thestringers 12 are oriented generally parallel to a longitudinal axis 18of the fuselage 10. It has been determined through testing and analysisthat this arrangement of frames and stringers produces a fundamentalpanel vibration mode shape for the skin panel 16 that is alignedgenerally parallel to a major streamline of the direction of theturbulent boundary layer. This is indicated in simplified fashion bydashed line 22, and the major streamline of the turbulent boundary layerflow is represented by arrow 20. It will be appreciated that thefundamental vibration mode shape is a natural response of the skin panel16 that is independent of the type of excitation acting on the skinpanel 16. In this example, portions 24 represent areas of displacementof the skin panel 16 that would be projecting slightly toward the reader(i.e., out of the paper), while areas 26 represent portions of the skinpanel 16 that would be displaced away from the reader (into the paper).The result is a fundamental panel vibration mode shape that is orientedparallel to the longitudinal axis 18 of the fuselage 10, and parallel tothe direction of the major streamline of the turbulent boundary layerflow 20 over the fuselage 10.

Referring now to FIG. 2, a preferred embodiment of a fuselage 100 isshown that is constructed in accordance with the principles of thepresent invention. Fuselage 100 includes a plurality of stringers 102interconnected with a plurality of frame members 104. Stringers 102 andframe members 104 are coupled generally perpendicular to one another.Stringers 102 can compromise I-beam stringers, blade type stringers, orany other suitable form of stringer. However, the stringers 102, insteadof being oriented generally parallel to the longitudinal axis 18 of thefuselage 100, are instead skewed so as to be oriented at an anglerepresented by arrow 106. Skin panel 108 is secured to the stringers 102and frame members 104 in any suitable fashion.

The orientation of the stringers 102 at an angle 106 relative to thedirection of flow of the major streamline of the turbulent boundarylayer 20 has been found to provide a fundamental panel vibration modeshape that is oriented non-parallel to the major streamline of theturbulent boundary layer flow 20. The fundamental panel vibration modeshape of the fuselage 100 is represented in simplified form by dashedline 110. For maximum noise level reduction, the orientation of thefundamental panel vibration mode shape 110 is preferably between about30°-45°, relative to the direction of the major streamline of theturbulent boundary layer flow 20. However, even some degree of noisereduction is achieved with the fundamental panel mode shape oriented atonly 5° relative to the major streamline of the turbulent boundary layerflow 20.

With the fundamental panel vibration mode shape oriented betweenapproximately 30°-45° relative to the direction of the major streamlineof the turbulent boundary layer flow 20, a noise reduction inside thefuselage 100 of at least about 2-3 dB can be realized for structuralskin panels with fundamental panel vibration mode natural frequenciesless than 500 Hz. This is due to the reduction in vibration of the skinpanel 108 over what would be experienced when the fundamental panelvibration mode shape is aligned parallel to the major streamline of theturbulent boundary layer flow 20. More specifically, this reduction invibration experienced by the skin panel 108 is largely associated withthe rapid decay of the turbulent boundary layer fluctuating pressurecorrelation characteristics in the span-wise direction.

Referring to FIG. 3, an alternative embodiment 200 of the fuselage isillustrated. The fuselage 200 similarly includes stringers 202 and framemembers 204 interconnected perpendicular to one another to form agrid-like supporting structure for an outer skin panel 206. However,diagonally placed stiffening members 208 are coupled in between thestringers 202 and the frame members 204. Stiffening members 208 maycomprise conventional I-beam type members, conventional blade typemembers or any other form of stiffening component, and are secured tothe skin panel 206, and serve to further stiffen the skin panel 206.When the stiffening members 208 are oriented at an angle that isnon-parallel to the direction of the major streamline of the boundarylayer flow 20, a fundamental panel vibration mode shape 210 is achievedwhich is also non-parallel to the direction of the major streamline ofthe turbulent boundary layer flow 20. The angle of the fundamental panelvibration mode shape 10 is preferably between about 30°-45° from themajor streamline of the turbulent boundary layer flow 20, and even morepreferably about 30°, relative to the direction of the flow 20. Again,orientating the fundamental panel vibration mode shape 210 at an angleof preferably about 30°-45° can result in a noise and vibration levelreduction within the fuselage 200 of at least about 1-5 dB. Even smallangles such as 5° will provide some level of noise and vibrationreduction, although the largest reductions are generally achieved atangles of about 30°-45°. Angles greater than about 30°-45° will providesome degree of noise attenuation but to a lesser extent than anglesbetween about 30°-45°.

The following analysis is intended to illustrate the effects of theangle of the major streamline of the turbulent boundary layer flowrelative to the fundamental panel vibration mode shape of the skin panel108 or 206. In the analysis, the major streamline of the turbulentboundary layer flow 20 was oriented at an angle to a simply supportedpanel. The term “simply supported” refers to the boundary condition atthe edge of the panel. For a simply supported panel, the edges are fixedin translation but allowed to rotate.

The velocity spectral density Φ_(vv)(ω), or vibration response, of apanel subjected to a random pressure field may be written as:

${\Phi_{vv}(\omega)} = {\sum\limits_{I}^{N}{{Y_{r}}^{2}{\Phi_{pp}(\omega)}A^{2}{j_{rr}^{2}(\omega)}}}$where |Y(ω)|² is the admittance matrix, Φ_(pp)(ω) is the spectraldensity of the fluctuating pressure, A is the surface area of the plateand j_(rr) ²(ω) is a non-dimensional value called the joint acceptance.The joint acceptance is a measure of the effectiveness of the complexpressure field in exciting a particular vibration mode of a structure.For any particular mode the joint acceptance is a real value that variesbetween zero and one. The vibration response of a panel either increasesor decreases as the joint acceptance of the structural mode increases ordecreases. A value of zero indicates that a structural mode is notexcited by the fluctuating pressure field and a value of one indicatesthat there is a perfect match between the fluctuating pressure field andthe structural mode. In other words, the lower the value of the jointacceptance, the lower the vibration response of the panel will be. Thejoint acceptance may be defined by:

j_(rr)²(ω)∫_(A) ∫_(A) C_(pp)(ω)ϕ_(r)(z)ϕ_(r)(z^(′)) 𝕕z 𝕕z^(′)/A²

where φ_(r) is the mode shape for a particular mode r and C_(PP)(ω) isthe narrow band space correlation coefficient of the fluctuatingpressure field.

The narrow-band space correlation coefficient C_(pp) of the turbulentboundary layer fluctuating pressure field is defined:

$\begin{matrix}{{C_{pp}(\omega)} = \frac{\Phi_{pp}\left( {\xi_{1},\xi_{2},\omega} \right)}{\Phi_{pp}(\omega)}} \\{= {\exp\left\lbrack {{- \frac{\xi_{1}}{\Lambda_{1}(\omega)}} - \frac{\xi_{2}}{\Lambda_{2}(\omega)} - \frac{{\mathbb{i}}\;\omega\;\xi_{1}}{U_{ph}(\omega)}} \right\rbrack}}\end{matrix}$

where |ξ₁| and |ξ₂| are the components of space separation vectorsbetween points (1) and (2) along the stream-wise axis direction x,|ξ₁|=|x₂−x₁| and span-wise axis direction y, |ξ₂|=|y₂−y₁|;

Λ₁(ω) and Λ₂(ω) are the correlation scales in vector directions ξ₁ andξ₂; and

U_(ph)(ω) is the phase velocity in vector direction ξ₁.

The level Φ_(pp)(ω), the spatial correlation constants Λ₁(ω) and Λ₂(ω),and the convection velocity U_(ph)(ω) are functions of the Strouhalnumber ωδ/U_(τ) where δ is the boundary layer thickness and U_(τ) is thedynamic velocity.

In general, the spanwise correlation scale Λ₂ is much smaller than thestreamwise correlation scale Λ₁. As a result, the spanwise components ofthe boundary layer flow are much less efficient than the streamwisecomponents in exciting a structural panel.

Mode shapes φ of a simply supported flat plate with length L and width Ware given by:

$\phi_{mn} = {\sin\frac{m\;\pi\; x}{L}\sin{\frac{n\;\pi\; y}{W}.}}$

where the mode indices m and n represent the number of half-waves in thex and y directions, respectively.

In developing the joint acceptance functions for the simply supportedplate it is reasonable to assume:j _(mn) ² =j _(m) ² ·j _(n) ²

where j_(m) ² and j_(n) ² are the joint acceptance functions for themode indices m and n, respectively. These terms are easily calculatedwhen the coordinate system of the simply supported plate is aligned withthe coordinate system for the turbulent boundary layer correlationcoefficients.

Referring to FIG. 4, when the coordinate system X′Y′ of the turbulentboundary layer flow is rotated relative to the coordinate system XY ofthe simply supported plate a coordinate transformation is firstperformed. The correlation parameters Λ₁, Λ₂ and U_(ph) in the X′Y′system are related to a rotated system XY as shown below:

U_(phX) = U_(ph)/cos  α U_(phY) = U_(ph)/sin  α$\frac{1}{\Lambda_{x}} = {\frac{\cos\;\alpha}{\Lambda_{1}} + \frac{\sin\;\alpha}{\Lambda_{2}}}$$\frac{1}{\Lambda_{y}} = {\frac{\cos\;\alpha}{\Lambda_{2}} + \frac{\sin\;\alpha}{\Lambda_{1}}}$

The narrow-band space correlation coefficient C_(pp)(ω) of the turbulentboundary layer fluctuating pressure field is now defined:

${C_{pp}(\omega)} = {\exp\begin{bmatrix}{{{- {X}}\left( {\frac{\cos\;\alpha}{\Lambda_{1}(\omega)} + \frac{\sin\;\alpha}{\Lambda_{2}(\omega)}} \right)} -} \\{{{Y}\left( {\frac{\cos\;\alpha}{\Lambda_{2}(\omega)} + \frac{\sin\;\alpha}{\Lambda_{1}(\omega)}} \right)} -} \\{\frac{{\mathbb{i}}\;\omega\; X\;\cos\;\alpha}{U_{ph}(\omega)} - \frac{{\mathbb{i}}\;\omega\; Y\;\sin\;\alpha}{U_{ph}(\omega)}}\end{bmatrix}}$In this equation |X| and |Y| are the components of space separationvectors between points (1) and (2) along the axis direction x,|X|=|x₂−x₁| and axis direction y, |Y|=|y₂−y₁| of the simply supportedpanel coordinate system. The equation represents the boundary layerpressure fluctuations on the outside of the aircraft.

Referring to FIG. 5, the joint acceptance function for the fundamentalpanel mode (m=1, n=1) of a simply supported plate was calculated atangles α.=0°, 5°, 10°, 15°, 30° and 45° for the case described below.

FIG. 6 shows the ΔdB reduction of the panel response for the variousflow angles. The reduction in panel response associated with a givenmode is simply the ratio of the joint acceptance with flow angle 0° tothe joint acceptance with flow angle α.

${\Delta\;{dB}} = {10\;\log\frac{{j_{11}^{2}(\omega)}_{o}}{{j_{11}^{2}(\omega)}_{\alpha}}}$Although the example is for a particular panel size and aircraft flightcondition, the invention is applicable to any structure having aboundary layer flow.

The reduction in panel response (or lack thereof) is a function of thenatural frequency of the panel. For a panel with a very low naturalfrequency there would be a reduction in panel response of up to 5 dB fora flow angle of 30°. For a panel mode natural frequency greater than 800Hz there would actually be a slight increase in the panel response dueto flow angle. Internal pressurization of an aircraft fuselage ataltitude is expected to produce a panel mode natural frequency ofapproximately 400 Hz for the skin panels described. At 400 Hz therewould be a 3 dB reduction associated with a 30° flow angle (i.e., afundamental panel mode shape oriented at 30° relative to the majorstreamline of the turbulent boundary layer flow). It is worthwhilenoting that even a small flow angle of 5° will lead to a 1 dB reductionat 400 Hz.

The individual components j_(x) ² and j_(y) ² of the joint acceptancefunction are shown in FIG. 7 and FIG. 8 for the various flow angles.Whereas the longitudinal component j_(x) ² quickly decays as a functionof flow angle, the lateral component j_(y) ² is fairly insensitive andincreases slightly with higher flow angles. This is attributed to therapid decay in the span-wise direction, as compared to the decay in thestream-wise direction, of the turbulent boundary layer fluctuatingpressure correlating characteristics.

Since it is the longitudinal component of the panel joint acceptancethat dominates the panel vibration reduction, the sensitivity to panellength was also investigated (FIG. 9). For a flow angle of 30° onlyslight differences are observed in the longitudinal component j_(x) ² ofthe joint acceptance as the panel length is varied. Thus, changes inpanel length are likely to have an insignificant effect on thepreviously calculated ΔdB reduction associated with flow angle.

The present invention thus enables noise and vibration to be reducedwithin a cabin or like structure of a fuselage of a mobile platformexperiencing a turbulent boundary layer flow over the outer skin panelof the fuselage. Forming the support elements of the fuselage in amanner that provides a fundamental panel vibration mode shape that isangled non-parallel to the direction of the turbulent boundary layerflow results in a noise reduction of at least about 1-5 dB at naturalpanel frequencies typically produced by the skin panel. For panelvibration mode frequencies less than about 500 Hz, a 3-5 dB reduction inpanel response is achieved for the larger angles. The direction of themajor streamline of the turbulent boundary layer flow could alsoinfluence noise and vibration on higher order modes other than thefundamental panel vibration mode. It is expected that higher order modeswill be somewhat less sensitive to changes in the direction of theturbulent boundary layer flow, but that nevertheless some further degreeof noise level reduction can potentially be achieved. Furthermore,internal pressurization of the cabin, such as that which occurs in acommercial aircraft, would likely have some impact on the fundamentalpanel vibration modes and this factor may further require tailoring ofthe precise orientation of the fundamental panel vibration mode relativeto the direction of the major streamline of the turbulent boundary layerflow to achieve maximum noise level reduction within the cabin.

The various embodiments referred to herein can potentially be used foran entire aircraft fuselage, or could instead be applied to localregions of the fuselage such as window belts or other areas formingrelatively high noise regions of a passenger cabin of an aircraft wherenoise resulting from the orientation of the fundamental panel mode is aprincipal contributing factor to the overall noise level experienced byoccupants of the mobile platform. An example of the teachings of thepresent application applied to just a window belt region 304 of afuselage 302 of a commercial jet aircraft 300. The invention couldeasily be applied to fuselage areas around a flight deck of the mobileplatform or other areas of the fuselage. Importantly, the presentinvention enables a significant degree of noise and vibration reductionto be achieved within an interior area of a commercial aircraft duringcruise conditions without the need for additional insulating material tobe incorporated within the fuselage, or alternatively may allow adesired degree of noise reduction to be achieved with less insulatingmaterial being required, as compared to a mobile platform having atraditionally constructed fuselage. This in turn avoids, or limits, theadded cost, weight and complexity of manufacture that would beintroduced simply by the use of additional insulating materials, andfurther helps to prevent a decrease in the fuel economy of the aircraftthat would likely be experienced from the added weight of extrainsulating materials.

Still further, while the various preferred embodiments have beenexplained in the context of an aircraft fuselage, it should beappreciated that any high speed land, sea based or airborne mobileplatform having a cabin-like interior area, and experiencing a turbulentboundary layer flow over an outer surface of the cabin area, canpotentially benefit from the teachings expressed in the presentapplication.

While various preferred embodiments have been described, those skilledin the art will recognize modifications or variations which might bemade without departing from the inventive concept. The examplesillustrate the invention and are not intended to limit it. Therefore,the description and claims should be interpreted liberally with onlysuch limitation as is necessary in view of the pertinent prior art.

What is claimed is:
 1. A method for reducing noise within a jetaircraft, wherein the noise is at least in part caused by a turbulentboundary layer flow of air over an outer surface of a skin of the jetaircraft, the method comprising: forming a fuselage of the mobileplatform with a plurality of stringers and a plurality of frame membersthe mobile platform comprising a jet engine able to attain an airspeedof about 500 mph; further forming the fuselage so that both theplurality of stringers and the plurality of frame members are orientednon-parallel to a longitudinal axis extending fore to aft along thefuselage; and securing a skin to the plurality of stringers and theplurality of frame members, for supporting the skin, wherein thenonparallel arrangement of the plurality of frame members and theplurality of stringers, relative to the longitudinal axis, provides afundamental vibration mode shape for the skin that is not parallel to adirection of flow of the turbulent boundary layer flow.
 2. The method ofclaim 1, wherein forming the fuselage comprises forming the structure sothat the stringers are disposed at an angle of between about 30-45degrees relative to the longitudinal axis, to create a fundamentalvibration mode shape which extends at an angle of between about 30degrees and 45 degrees to the direction of flow of the turbulentboundary layer.
 3. The method of claim 1, wherein said structure isfurther formed with at least one stiffening member placed diagonallybetween one of the stringers and one of the frame members.
 4. The methodof claim 1, wherein forming the fuselage with a plurality of stringerscomprises forming the fuselage with a plurality of at least one ofI-beam stringers and blade stringers.
 5. A method for reducing noise andvibration within a fuselage of a jet aircraft, wherein the noise andvibration are at least in part caused by airflow over an outer skin ofthe jet aircraft parallel to a longitudinal line extending fore to aftalong the fuselage of the jet aircraft, the method comprising: forming afuselage for the jet aircraft with a plurality of stringers and aplurality of frame members such that the plurality of stringers isoriented parallel to the longitudinal line the fuselage being suited toenable the aircraft to be operated at an airspeed of about 500 mph;further forming the fuselage with a plurality of stiffening members thatare oriented at an angle non-parallel to the longitudinal line,non-parallel to the plurality of stringers and non-parallel to theplurality of frame members; securing a skin panel to the pluralities ofstringers, frame members and stiffening members; and using thenon-parallel orientation of the stiffening members relative to thelongitudinal line to create a fundamental panel vibration mode shape forthe skin of the fuselage that is not parallel to the longitudinal line,to cause a noise reduction within an interior area of the fuselage ofnoise generated by airflow over the skin of the fuselage while the jetaircraft is in flight.
 6. The method of claim 5, wherein the pluralityof stiffening members are each secured at an angle of at least about 30degrees relative to the longitudinal line.
 7. The method of claim 6,wherein forming the fuselage comprises arranging the plurality ofstiffening members such that each one of the plurality of stiffeningmembers is secured at an angle of between about 30 degrees and 45degrees relative to the longitudinal line.
 8. The method of claim 5,wherein forming the fuselage comprises arranging the plurality ofstiffening members such that each one of the plurality of stiffeningmembers is secured non-parallel to the longitudinal line but not morethan about 45 degrees relative to the longitudinal line.
 9. The methodof claim 5, wherein forming the fuselage comprises arranging theplurality of plurality of stringers perpendicular to the plurality offrame members.
 10. The method of claim 5, wherein forming the fuselagewith the plurality of stringers comprises forming the fuselage with atleast one of: a plurality of I-beam stringers; and a plurality of bladestringers.